Sequence detection by multi-valued coding and creation of multi-code sequences

ABSTRACT

Methods of coding and correlating sequences are disclosed. The methods of coding and correlating are applied to binary sequences to convert these into multi-value sequences to improve the ability to recognize a sequence. Received sequences may contain errors. Coding methods and lengths of coding runs to improve detection and rejection of sequences are also disclosed. Methods for calculating correlation values are also disclosed. Higher-value coding of lower value sequences, wherein the lower value sequences are non-binary is disclosed. Symmetrical and asymmetrical coding methods are disclosed. Multi-code sequences are described and methods to create multi-code sequences by using gates and inverters are disclosed. Methods for the detection of multi-code sequences by using descramblers are also disclosed.

STATEMENT OF RELATED CASES

This patent application claims the benefit of U.S. Provisional PatentApplication No. 60/575,948, filed on Jun. 1, 2004, entitled MULTI-VALUECODING OF SEQUENCES AND MULTI-VALUE MEMORY DEVICES and U.S. ProvisionalPatent Application No. 60/668,355, filed Apr. 5, 2005, entitled IMPROVEDSEQUENCE DETECTION BY MULTI-VALUE CODING, both of which are incorporatedherein fully by reference.

BACKGROUND OF THE INVENTION

The present invention relates to the creation, coding, processing anddetection of sequences comprised of binary and multi-value digital(non-binary) symbols. One aspect of the present invention relates toimproved detection of sequences as well as the improved distinguishingbetween sequences.

Another aspect of the invention relates to the creation of signalswherein individual sequences represent one of n symbols with n aninteger greater than 2.

The present invention has application in telecommunication systems,control systems and other applications. A specific example of where thepresent invention has utility includes spread-spectrum technologies inthe transmission and the detection of data signals.

The present invention relates to multi-valued coding of sequences. Asequence is a series of digital symbols which can be represented in asignal consisting of separate elements or symbols (sometimes calledchips) with discrete and distinguishable values. For the purpose ofsimplicity discrete values of signals will be represented here asnumbers in origin 0 or as amplitude of a signal. It should be clear thatother physical properties, for example a pulse position or the phase ofa carrier signal or the polarization of a carrier signal can be used torepresent the discrete elements in a sequence. It should also be clearthat representation of the symbols as numbers is for convenience only.

In current applications of spread spectrum technologies used for thetransmission of signals, such as in wireless communications, a digitaldata symbol is translated into a sequence consisting of a certain numberof binary symbols. The transmission of the sequence will usually beachieved in the same time as the duration of the original data symbol.Instead of sending or receiving one specific discrete signal thatrepresents a data symbol one will send or receive a sequence of (in thiscase) binary symbols. The generated sequence consists of multiplesymbols (also called chips), as opposed to the single data element, andit is said that the signal is ‘spread’.

To enable correct reception of the spreaded data elements each of theoriginal data elements has to be coded by a different sequence, so thatat the receiving end it can be determined which data symbol was sent. Ifdifferent users of a transmission system occupy the same physicalchannel (such as in radio communications), then distinguishing betweenthe symbols from each individual user requires the assignment ofdifferent sequences for the each symbol sent by each user. In presentsystems, the data symbols are generally binary (0 or 1) and therepresenting sequences also consist of binary symbols.

A common system for detecting the presence of a certain sequence in areceived signal is by way of correlation. This method involves thegeneration of the to be detected sequence at the receiving end, andcomparing this locally generated sequence with the received signal.

The principle of correlation between two sequences for detection andsynchronization works in such as way that the assigned values ofconsecutive elements in two sequences will be multiplied and the resultadded to a sum. When two sequences are synchronized and identical thesum reaches a maximum value. When the two sequences are different or arenot synchronized the sum ideally should be lower than when the sequencesare identical and synchronized.

This discrete form of correlation is generally expressed in formula as:${C(j)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\quad{a_{i}{a_{i + j}.}}}}$This expression determines the (normalized) autocorrelation of thesequence A with N elements a_(i). For the (normalized) cross-correlationof two different sequences A and B with N elements a_(i) and b_(i) thefollowing expression determines the cross-correlation:${C(j)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\quad{a_{i}b_{i + j}}}}$

The correlation method can be used to synchronize the locally generatedsequence with a known received sequence by “searching” for an alignmentwherein the correlation value between the two sequences has or exceeds acertain value.

The correlation method can also be used for detection of a certainsequence when it is part of a received sequence. In that casesynchronization of the locally generated sequence with the receivedsequence should be assured. Also the correlation value of the receivedand the locally generated sequence should be equal to or exceed acertain value when the two sequences are identical.

Such a system for receiving and detecting sequences is less sensitive tonoise and errors when the correlation value is high when sequences aresynchronized and identical and very low when sequences are different ornot synchronized. The known way to achieve a certain correlationperformance is to use a selected group of binary sequences, wherein theautocorrelation shows a single high peak and the crosscorrelation islow. It is known from the literature that binary m-sequences orpseudo-random sequences have such a performance.

The present approach limits the number of usable sequences inapplications such as communication systems. There is a need for a methodto detect sequences that do not comply with certain statisticalrequirements. Such a novel method is one aspect of the presentinvention.

The properties of pseudo-random and other digital sequences aredocumented and widely used in present communication systems. It may benecessary (for instance for security reasons or in heavily congestedsituations) to make sequences look more alike and less distinguishablefor present methods, while still being able to distinguish between thesequences. This is another aspect of the present invention.

A novel way is to increase the correlation value when elements areidentical and subtract a higher value when elements are not equal. Thismethod was described by the inventor in U.S. Non-Provisional patentapplication Ser. No. 11/042,645, filed Jan. 25, 2005, entitledMULTI-VALUED SCRAMBLING AND DESCRAMBLING OF DIGITAL DATA ON OPTICALDISKS AND OTHER STORAGE MEDIA and in U.S. Non-Provisional patentapplication Ser. No. 11/065,836 filed Feb. 25, 2005, entitled GENERATIONAND DETECTION OF NON-BINARY DIGITAL SEQUENCES; both are incorporatedherein by reference.

A novel way to determine and improve the correlation performance fordetection of sequences is one aspect of the present invention.

It is clear to the inventor that detection of a sequence is determiningif a received sequence has a certain number of elements in a certainorder. Correlation methods in essence execute only one part of thatprocess: it determines if a received sequence has the same number ofcertain elements as the to be detected sequence.

Binary maximum length or m-sequences have an equal or almost equalnumber of ‘0’ and ‘1’ symbols. Their distribution over the sequence issuch that there is only one position in the autocorrelation graph whereall symbols are aligned. In all other shifted (or not-synchronized)positions there is almost an equal number or matching and non-matchingsymbols.

It should be clear that for binary sequences wherein either the ‘0’symbols or the ‘1’ symbols dominate in a significant way the differencebetween the highest and lowest correlation values will be smaller thanwhen the there are close to equal numbers of ‘0’ and ‘1’ symbols.

Binary sequences that ‘look alike’ or that have a relatively greatnumber of identical symbols at corresponding positions are difficult todistinguish from each other. The present invention addresses theseshortcomings and limitations in present and prior art.

Sequences presently used in spread-spectrum applications arepredominantly of a binary nature. Also a sequence of binary symbolspre-dominantly represents a binary symbol. It is known that a sequenceof m binary symbols can represent an n-valued symbol, for n≦2^(m). Thismethod of assigning more than 2 symbols to a sequence for one user isalso known as Multi-coding.

It is another aspect of the present invention to provide a method tocreate and detect multi-code sequences.

SUMMARY OF THE INVENTION

In view of the more limited possibilities of the prior art in use inbinary spread spectrum technology of certain sequences because they aretoo similar to others, one aspect of the current invention offers animprovement of distinguishing between sequences. Another aspect islimiting the effect of sequence errors.

The general purpose of the present invention, which will be describedsubsequently in greater detail, is to provide methods of multi-valuecoding of digital sequences, such as used in spread spectrum technologyand improve sequence detection methods.

Before explaining at least one embodiment of the invention in detail, itis to be understood that the invention is not limited in its applicationto the details of construction and to the arrangements of the componentsset forth in the following description or illustrated in the drawings.The invention is capable of other embodiments and of being practiced andcarried out in various ways. The methods can be implemented in andexecuted by digital circuitry with or without A/D and D/A converters.The methods can also be executed by computer programs inmicro-processors, digital signal processors or general computingequipment, with or without help of A/D and D/A converters. The methodscan also be executed by multi-valued digital circuitry. For illustrativepurposes binary symbols are represented as 0 and 1. A binary 0 may bemulti-value coded as 0, 1 and 2 while a 1 may be multi-value coded as 4,5 and 6. It should be clear that symbols represent logic states and notarithmetical numbers. Values may be assigned to states and used incorrelation processes. However value assignments are arbitrary and maybe selected on different preferences. Also, it is to be understood thatthe phraseology and terminology employed herein are for the purpose ofthe description and should not be regarded as limiting.

Multi-value and n-value in the context of this application mean a numbern, with n being a positive integer greater than two. A primary object ofthe present invention is to provide a new method for transmitting andreceiving binary and multi-value digital symbols in spread spectrumtechnology that will overcome the shortcomings of the prior arttechnology.

An object is to provide a method of multi-value coding of binarysignals.

Another object is to apply multi-value coding of a binary signal toadjust the autocorrelation of a signal.

Another object is to apply multi-value coding of two binary signals toadjust the correlation between the two signals.

Another object is to use the method of multi-value coding of binarysignals and correlation adjustment to make the differences betweensequences more pronounced and consequently make it easier to distinguishbetween sequences.

Another object is to provide a method to create multi-code sequences.

Another object is to provide a method to detect a particular sequence ina multi-code sequence.

In accordance with another aspect of the present invention, a method ofcoding a first sequence of binary numbers to create a first sequence ofmulti-value numbers, is provided. In the method, each binary number inthe sequence of binary numbers is sequentially evaluated as follows. Ifthe binary number is the first 0 encountered, a 0 is placed in the firstsequence of multi-value numbers. If the binary number is the second 0encountered, a 1 is placed in the first sequence of multi-value numbers.If the binary number is the third 0 encountered, a 2 is placed in thefirst sequence of multi-value numbers, and the process then begins tolook for the first 0 encountered when sequentially evaluating eachbinary number.

If the binary number is the first 1 encountered, a 3 is placed in thefirst sequence of multi-value numbers. If the binary number is thesecond 1 encountered, a 4 is placed in the first sequence of multi-valuenumbers. If the binary number is the third 1 encountered, a 5 is placedin the first sequence of multi-value numbers and the process then beginsto look for the first 1 encountered when sequentially evaluating eachbinary number.

The previous multi-valued coding scheme for binary sequences is anexample for illustrative purposes only. Different schemes to code 0s and1s with multi-valued elements may be selected. This may includedifferent lengths of 0s and/or 1s to be coded. Similar schemes can alsobe developed and applied to code n-valued sequences with p-valuedelements with p greater than n.

BRIEF DESCRIPTION OF THE DRAWINGS

Various other objects, features and attendant advantages of the presentinvention will become fully appreciated as the same becomes betterunderstood when considered in conjunction with the accompanyingdrawings, and wherein:

FIG. 1 is a graph showing an autocorrelation of a 20 elements binarysequence;

FIG. 2 is a diagram of a multi-value coding and correlation method;

FIG. 3 is a graph showing the correlation according the method of FIG. 2applying 4-value coding of the sequence used for FIG. 1;

FIG. 4 shows a graph combining the graphs of FIG. 1 and FIG. 3;

FIG. 5 is a graph showing the correlation of the 6-value coded binarysequence used for the graph of FIG. 1;

FIG. 6 shows the combination of the correlation graphs for the uncoded,the 4-value coded and the 6-value coded binary sequence;

FIG. 7 shows the correlation graph of an asymmetrical 4-value codedbinary sequence;

FIG. 8 is a graph showing the cross-correlation between two binarysequences;

FIG. 9 is a graph combining the correlations of individual and betweentwo 4-value coded binary sequences;

FIG. 10 is graph showing the correlation of the 4-value coded sequencesof FIG. 9 using a different correlation method;

FIG. 11 is graph showing the correlation of 4-value coded binarysequences, wherein the second sequence is a copy of the first sequencewith an inverted first element;

FIG. 12 is a graph of the 4-value coded sequences of FIG. 11 with alimited coding run of 6 elements;

FIG. 13 is a graph showing the autocorrelation of one of two uncodedternary sequences and the crosscorrelation between the two ternarysequences;

FIG. 14 is a graph of the correlation of the 6-value coded ternarysequences of FIG. 13;

FIG. 15 a shows a block diagram to generate a multi-code binarysequence;

FIG. 15 b shows the diagram of FIG. 15 a with application of gates andinverters;

FIG. 16 a shows a diagram of an individually controlled gate;

FIG. 16 b shows another diagram of an individually controlled gate;

FIG. 16 c shows a diagram of a ternary inverter;

FIG. 16 d shows another diagram of a ternary inverter;

FIG. 17 shows a diagram of a multi-code sequence detector applyingcorrelators;

FIG. 18 shows a diagram of a multi-code sequence detector applyingdescramblers;

FIG. 19 a shows a diagram of an LFSR based sequence generator;

FIG. 19 b shows the matching descrambler for the circuit of FIG. 19 a;

FIG. 20 a shows a diagram of an LFSR based sequence generator;

FIG. 20 b shows the matching descrambler for the circuit of FIG. 20 a;

FIG. 21 a shows a diagram of an LFSR based sequence generator;

FIG. 21 b shows the matching descrambler for the circuit of FIG. 21 a;

DETAILED DESCRIPTION AND PREFERRED EMBODIMENT OF THE INVENTION

Multi-Value Coding of Binary Sequences and the Effect on Correlation.

There are several methods to detect a sequence. Which one to use will bedictated by the statistical properties of the sequence or the way theyare generated. It is clear to the inventor that detection of a sequencecomprises determining if a received sequence has a certain number ofelements in a certain order. Correlation methods in essence execute onlyone part of that process: they determine if a received sequence has thesame number of certain elements as the to be detected sequence.

Correlation in essence ignores the order of elements. When correlationdetermines that two sequences have exactly the same number of differentelements, it can be concluded that the two sequences are identical. Whenfor instance 80% of the elements of two sequences are identical there isa chance that the sequences are identical, but that a certain number ofelements where not correctly detected or experienced noise effects.However there is also a chance that the sequences were different, butjust coincided on certain elements in such a way that a high correlationvalue was achieved.

A novel way to detect sequences is to increase the correlation valuewhen elements are identical and decrease the correlation with a highervalue when elements are not equal. This method was described by theinventor in U.S. Non-Provisional patent application Ser. No. 11/042,645, filed Jan. 25, 2005, entitled MULTI-VALUED SCRAMBLING AND DESCRAMBLINGOF DIGITAL DATA ON OPTICAL DISKS AND OTHER STORAGE MEDIA.

Another novel way to determine and improve the correlation performancefor detection of sequences is one aspect of the present invention.According to this aspect of the present invention the level ofconfidence in detecting a sequence can be improved by considering theorder of elements in a sequence and not just the number of elements.This can be achieved by applying a multi-value coding method to both thesequence that is being received and to the locally generated sequence.

Further improvement of the correlation performance can be achieved byapplying different correlation methods.

The method of multi-value coding of sequences will be explained by wayof illustrative examples. It should be clear that these examples are forillustrative purposes only and do not limit the application or reach ofthe present invention.

Assume the following binary sequence with 20 elements: bin=[1 0 0 1 0 11 1 1 1 1 0 0 1 0 1 1 0 1 0]. FIG. 1 shows the autocorrelation graph ofthis sequence. The correlation is determined by adding 1 to a sum whenelements are identical and subtracting 1 when the elements are notidentical.

The multivalue coding scheme is schematically shown in FIG. 2. A locallygenerated, to be detected sequence is inputted on an input 201 to amulti-value coder 202. The resulting multi-value coded sequence isoutputted on input 203 of a comparator and adder 207. A receivedsequence is inputted on an input 204 of a multi-value coder 205.Multi-value coders 202 and 205 apply exactly the same multi-value codingmethod. The multi-value coder 205 outputs a multi-value coded sequenceon input 206 to the comparator and adder 207. The comparator/adder 207is reset at 0 at the start of a new detection cycle. A controlling clockmay be used to determine the moment of coding, comparing and adding.After completion of the to be detected sequence, the sum available atoutput 208 reflects the correlation value between the two multi-valuecoded sequences.

One multi-value coding scheme can be the following:

1. code a first 0 as a 0

2. code a second 0 as a 2

3. code a third 0 again as a 0

etc.

a. code a first 1 as a 1

b. code a second 1 as a 3

c. code a third 1 again as a 1

etc.

According to the above coding scheme the sequence:

bin=[1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0] will be coded as

bin4=[1 0 2 3 0 1 3 1 3 1 3 2 0 1 2 3 1 0 3 2]

One can create the correlation graph of bin4, based on the method that a1 is added to the correlation value when elements are identical and 1 issubtracted when they are different. The correlation graph is shown inFIG. 3 and could be created by inputting sequence bin4 on 201 andinputting shifted versions of bin4 on input 204 of FIG. 2. It should beclear that this graph is not an autocorrelation graph of bin4. Thereason for that is that every shifted version of bin will be coded bycoder 205 in FIG. 2. A coded version of a shifted sequence is in manycases not the same as the shifted version of a coded sequence.

FIG. 3 is the correlation graph between the 4-value coded sequence bin4and the 4-value coded sequences of its shifted versions. FIG. 4 showsthis graph combined with the autocorrelation graph of sequence bin. Itshows that the 4-value coded sequence has a better correlationperformance, though two sub-peaks (though lower than in theautocorrelation graph) still remain.

One can further improve the correlation performance by applyingadditional level of coding. For instance the sequence bin and itsshifted versions can be coded using the following rules:

1. code a first 0 as a 0

2. code a second 0 as a 2

3. code a third 0 as a 4

4. code a fourth 0 again as 0

etc.

a. code a first 1 as a 1

b. code a second 1 as a 3

c. code a third 1 as a 5

d. code a fourth 1 again as a 1

etc.

By applying the above rules, the sequence

bin=[1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0]

will then be coded into:

bin6=[1 0 2 3 4 5 1 3 5 1 3 0 2 5 4 1 3 0 5 2]

FIG. 5 provides the correlation graph of the 6-value coded binarysequence applying the approach as provided schematically in FIG. 2. Itshows that the two sub-peaks have almost disappeared and except for thesynchronization peak, all other correlation values are well below 0.FIG. 6 provides the combined graphs of the binary (uncoded) correlation,the 4-value coded correlation and the 6-value coded correlation.

The examples apply a symmetrical coding mechanism, wherein both the 0and the 1 symbols are coded into an equal number of additional states.This is not necessary or always desirable and depends on the statisticalqualities of the binary sequences.

For instance one can design the following 4-value coding rule:

1. all 0 will be coded as a 0

2. a first 1 will be coded as a 1

3. a second 1 will be coded as a 2

4. a third 1 will be coded as a 3

5. a fourth 1 will again be coded as a 1

etc.

The result of applying this coding rule to the binary sequence:

bin=[1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0] will create

bin41=[1 0 0 2 0 3 1 2 3 1 2 0 0 3 0 1 2 0 3 0]

The correlation graph of the sequence bin41 with a shifted and thencoded version of bin is shown in FIG. 7. Compared to the correlationgraph shown in FIG. 4, which is the result of a different 4-value codingscheme, this correlation graph shows a better performance, as is has nosignificant sub-peaks.

The correlation of a coded sequences with a shifted and then codedversion of itself is important for positive detection (orsynchronization). However it is also important to prevent a “false”detection. This means that sequences that are coded and correlated withand different from a locally generated and multi-value coded sequenceshould generate a low correlation value.

One advantage of comparing two non-binary sequences is that there aremore and different possible combinations between elements. In a binarysystem the only ‘not equal’ combination is {0, 1}, which is treated thesame as {1, 0}. In a ternary coding with elements 0, 1 and 2 the ‘notequal’ combinations are {0, 1}, {0, 2} and {1, 2}. As explained in U.S.Non-Provisional patent application Ser. No. 11/042,645, filed Jan. 25,2005, entitled MULTI-VALUED SCRAMBLING AND DESCRAMBLING OF DIGITAL DATAON OPTICAL DISKS AND OTHER STORAGE MEDIA one can use the differentcombinations to affect the correlation when two elements are not equal.

One can apply this method also to situations when elements of twomulti-value sequences are equal, and add a number that represents thevalue of the element. This can greatly enhance the peak value of thecorrelation graph. However it also enhances unwanted peaks in thecorrelation graph.

In order to demonstrate the effects of multi-value coding of binarysequences and the effects of different correlation methods the twofollowing sequences will be auto-correlated and cross-correlated witheach other using the here invented methods.

bin=[1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0]

bin2=[1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1]

FIG. 8 shows the correlation graphs for the two binary sequences, usinga standard correlation scheme by adding 1 when two elements areidentical and subtracting 1 when they are different. Thecross-correlation graph is the thick solid line, superimposed on thethin lines showing the individual autocorrelation graphs. Thecross-correlation has high peaks, almost as large as the synchronizedcorrelation peak. This is not very attractive for detection use.

FIG. 9 shows the correlation graphs for the two sequences applying thesymmetrical 4-value coding method for the two binary sequences. Thethick line again shows the cross-correlation, which is much better thanthe previous case. The thin lines are the individual correlation graphsusing 4-value coding. The peaks in the cross-correlation graphs havediminished substantially, so the chance to make a ‘wrong’ decisionbetween detecting the two sequences has diminished also.

One can apply the correlation method wherein a 1 is added when elementsare identical and the value of the compared to element is subtractedwhen the elements are different. It should be clear that this methoddoes not make a difference in the binary case. However in the 4-valuecase it makes a significant difference as shown in FIG. 10. The solidthick line is again the cross correlation between the 4-value codedbinary sequences. All cross-correlation values are now less than 0. Thismeans that a combination of multi-value-coding combined with novelcorrelation methods can significantly improve performance for detectionof certain (perhaps initially considered undesirable) sequences.

Effect of Element Errors.

It is known that disturbances such as noise may affect signals. Thedisturbance can be so severe that a signal may not be detectedcorrectly. For instance a 0 may be detected at the receiver as a 1 or a1 may be detected as a 0. The error performance of a digital (binary)channel is usually expressed as a bit-error-ratio (or BER). It may beassumed that channel BERs are better than 1 in 1000. However if a dataelement is represented in sequences of a length of 1000 or more, thenthe effects of a BER on the detection may be significant. An error in asequence element may occur at the beginning of a sequence. This meansthat the whole sequence may be 4-value coded in such a way that it willnot be detected in the correlation phase.

A way to prevent that is to allow multi-value coding run for only alimited number of sequence elements and reset the starting point of thecoding process. This means that the effect of a bit error in a receivedsequence will be limited to the single coding run where the erroroccurred.

It should be clear that sequences like bin and bin2 will not performwell with 4-value coding under occurrence of errors even with limitedcoding runs. To demonstrate the effect of errors and coding runs thefollowing two 50 bit sequences will be used:

binnew=[0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 01 1 1 0] and

binnen=[1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 10 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0]

Assume that an error occurs in the first bit of the sequence binnen.Instead of a 1 a 0 is detected. If the 4-value coding run is not limitedthe error will propagate through the whole sequence. The selected lengthof the 4-value code run depends on the expected error ratio and thestatistical properties of the binary sequences. If the code run lengthis too short the distinguishing properties of the method will bediminished. If the length of the code run is too long, then errors inthe beginning of a sequence will severely affect the ability to stilldetect the sequence when it is in the proper synchronization phase withthe locally generated sequence.

The 4-value symmetrically coded versions of the sequence binnen and ofbinner (being binnen with an error in the first bit) are shown:

binnen=[1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 10 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0]

binner=[0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 10 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0]

4-value coded with 25 elements coding run:

binnen4=[1 3 1 3 0 1 2 0 2 3 0 1 2 0 2 3 0 1 3 1 2 0 3 2 1 0 0 1 3 2 0 12 3 1 0 2 0 3 1 3 1 2 0 2 3 0 1 3 2]

binner4=[0 1 3 1 2 3 0 2 0 1 2 3 0 2 0 1 2 3 1 3 0 2 1 0 3 0 0 1 3 2 0 12 3 1 0 2 0 3 1 3 1 2 0 2 3 0 1 3 2]

The correlation method (using add 1 when identical and subtract thevalue of the compared to element when different) applied to theautocorrelation of binnen4 and the correlation between binnen4 and ashifted and then coded version of binner will generate the correlationgraphs as shown in FIG. 11. The thin dotted line shows theautocorrelation of binnen4. The thick line shows the correlation betweenthe coded version of binnen and the coded version of the shifted versionof binner. It clearly shows that the coding method discriminates verywell. However in this case such discrimination is not desirable.

A balance can be found in reducing the coding run to 6. The resultingcorrelation between sequences binnen and binner is shown in FIG. 12 asthe thick line. The synchronization peak is lower than the 50 whichwould be found when no error would have happened. However the peak isstill significantly higher than the other correlation values. Thecorrelation between binner and binnew is shown in FIG. 12 as the thinline. The peaks of these values are higher than when no error would havehappened. However they are still significantly below 0 and should notcause detection mistakes.

Multi-Value Coding Schemes.

Several multi-value coding schemes for binary sequences according todifferent aspects of this invention have been shown. It should be clearthat other variants and different multi-value coding schemes can beapplied. Such schemes depend on the expected sequences, the statisticaland error performance of the transmission channel, if independent means(like pilot or synchronization sequences) are available. For instancewhen the moment of synchronization is always known, the multi-valuescheme can be strictly applied to distinguish between presence andabsence of a sequence.

The presence of a sequence may be established by determining that other,known, sequences cannot be present. Knowledge or information aboutexpected error performance can be used to determine the length of codingruns as well as correlation methods.

Higher-Value Coding of Multi-Value Sequences.

It should be clear that the process of higher-value coding according tothe present invention can also be applied to non-binary sequences. Forillustrative purposes higher-value coding will be applied to two3-valued or ternary sequences. To those skilled in the art it should beclear that the methods here described can be applied to all sequenceswith n-valued elements and with n an integer greater than 2.

Assume the following 3-value or ternary sequences with 40 elements:

ter1=[0 1 2 2 1 0 0 0 1 2 1 2 2 0 2 1 0 1 1 2 1 1 0 2 1 2 0 2 2 2 2 1 10 1 2]

and

terr=[2 1 1 0 2 1 2 0 2 2 2 2 1 1 0 1 0 0 0 2 2 2 1 1 0 2 2 2 1 0 1 2 01 0 0]

FIG. 13 shows the autocorrelation graph of ter1 in a thin line and thecross-correlation of ter1 and terr as the thick line. The appliedcorrelation method is: add 1 when elements are identical, subtract 1when they are different. The cross-correlation graph has peaks wellabove 0.

The following 6-value coding will be applied to ter1 and shiftedversions of terr:

1. code the first 0 as 0

2. code the second 0 as 3

3. code the third 0 as 0 again

etc.

a. code the first 1 as 1

b. code the second 1 as 4

c. code the third 1 as 1 again

etc.

A. code the first 2 as 2

B. code the second 2 as 5

C. code the third 2 as 2 again

etc.

The result of this coding scheme applied to ter1 and ter2:

ter16=[0 1 2 5 4 3 0 3 1 2 4 5 2 0 5 1 3 4 1 2 4 1 0 5 4 2 3 5 2 5 2 1 40 1 5]

and

terr6=[2 1 4 0 5 1 2 3 5 2 5 2 4 1 0 4 3 0 3 5 2 5 1 4 0 2 5 1 4 3 1 2 04 3 0]

FIG. 14 shows a combined correlation graph. The thin solid line is theternary autocorrelation graph for ter1. The thin dotted line is thecorrelation graph for the 6-value coded sequence ter1 with shiftedversions of itself and applying the correlation method: add 1 whenelements are the same and subtract 1 when different. The solid thickline shows the correlation between the 6-value coded sequence ter1 andterr. The cross-correlation performance of the 6-value coded sequencesis considerable better than between the original uncoded ternarysequences.

As many apparently different embodiments of this invention may be madewithout departing from the spirit and scope thereof, it is to beunderstood that the invention is not limited to the specific embodimentsthereof. One embodiment of the creation of sequences representingnon-binary symbols is by applying n-value gates and inverters anddescribed in detail in provisional patent application 60/547683. It isknown from the literature and previously granted patents (see, forexample, U.S. Pat. No. 6,133,754) that it is possible to realize thosespecific devices (gates and inverters) in standard CMOS technology.

One embodiment of the execution of the multi-value coding of binarysequences is by applying and programming general Digital SignalProcessors (or DSPs). All values can be represented and manipulated inbinary form representing their respective required values.

Another embodiment is to realize the n-value devices in binary ROM orlook-up devices with the inputs being transformed by Analog/Digitalconverters and the output by Digital/Analog converters.

Coding of Multi-Valued Symbols into Binary and n-Valued Sequences.

Aspects of the present invention as described in this and followingsections claims the benefit of U.S. Provisional Patent Application No.60/575,948, filed on Jun. 1, 2004, entitled MULTI-VALUE CODING OFSEQUENCES AND MULTI-VALUE MEMORY DEVICES which is incorporated herein byreference.

Presently spread-spectrum sequences are predominantly binary in nature.Each individual sequence is different from other used sequences andrepresents a single binary data symbol. Spread spectrum sequences may beconsidered a code expansion of a symbol and contain a significant amountof redundancy.

Presently spread spectrum signals when received are matched with alocally generated copy of a corresponding sequence to determine thenature of the received sequence. If all or most of the elements (orchips) of the received sequence and the locally generated sequence matchit is decided that the received sequence is identical to the locallygenerated sequence. A circuit will then generate the binary symbol thatis represented by the received sequence.

One aspect of this invention provides a means to transmit higherinformation content per sequence. It does so by assigning a greaterrange of symbols to sequences and creating the composite sequence byusing individually controlled gates. Instead of assigning just 0 or 1,it now adds (as an example) the symbol 2 as an assigned symbol to asequence. This can be expanded to any number of symbols as long assequences are available, which depends of course on the length of asequence.

The method to assign more than two symbols to a binary sequence is knownas Multi-code Direct Sequence Spread Spectrum technology or MC-DSSSspread. In general MC-DSSS sequences are selected to be orthogonal.

The basic configuration for creating a sequenced binary signalrepresenting three symbols is shown in FIG. 15 a. There are threeindividual sequences, each representing one of three symbols. When thesystem detects a to be transmitted data symbol a gating device insertsthe appropriate representing sequence into the to be transmitted signal.

A more detailed picture is shown in FIG. 15 b. This configurationapplies the gates and inverters as described in U.S. Non-Provisionalpatent application Ser. No. 10/935,960, filed on Sep. 8, 2004, entitledTERNARY AND MULTI-VALUE DIGITAL SCRAMBLERS, DESCRAMBLERS AND SEQUENCEGENERATORS and U.S. Non-Provisional patent application Ser. No.11/000,218, filed Nov. 30, 2004, entitled SINGLE AND COMPOSITE BINARYAND MULTI-VALUED LOGIC FUNCTIONS FROM GATES AND INVERTERS, both of whichare incorporated herein fully by reference.

A device 1509 in the diagram of FIG. 15 b, possibly being a 4B3T coder,generating 3 ternary symbols from 4 binary symbols, creates a ternarysignal on input 1501. Input 1501 provides a control signal toindividually controlled gates 1505, gate 1506 and gate 1507. Details ofthis type of gate are shown in FIG. 16 a. When a control signal Con on acontrol input is equal to 0, the gate conducts between an input In andan output Out. An inverter in the control input to gate 1506 assuresthat a signal 1 is transformed into a 0, as is shown in FIG. 16 c. Thismeans that when the signal provided on 1501 in a 1 then only the gate1506 is conducting and the signal generated by 1503 will be outputted on1508.

The control input to gate 1507 has an inverter that will transform a 2into a 0. This inverter is shown in FIG. 16 d. This means that when thesignal provided by 1501 is a 2 then only gate 1507 is conducting and thesequence generated by 1504 will be outputted on 1508.

When the signal provided by 1501 is 0 then only gate 1505 is conductingand the sequence generated by 1502 will be outputted on 1508.

Consequently when a certain data element is present on 1501 itautomatically opens the corresponding gate and allows the correspondingsequence to be inserted for transmission on output 1508.

The relevant clock signals have been omitted to limit complexity of thefigures. However in certain configurations clock signals have to beapplied to ensure that start of a data-symbol and the beginning of itscorresponding sequence coincide.

It should be clear that this approach can be expanded to any n-valuedsymbol sequence insertion, provided sufficient distinguishing sequencesare available.

The approach can also be used to create composite n-valued sequencesrepresenting m different symbols.

A possible configuration for the detection and generation of therecovered data signal by way of correlation is shown in FIG. 17. It isassumed that all sequences are synchronized and that the start positionof all relevant sequences can be determined unambiguously. There areknown ways to achieve that.

A received sequence, representing a plurality of symbols is provided inthe circuit of FIG. 17 on input 1701. The signal on this input isprovided to three different correlation units 1702, 1703 and 1704. Unit1702 correlates the received sequence with sequence 1705, representingsymbol 0. When this sequence is detected as being present in thesequence provided by 1701 then the correlation unit 1702 generates asignal not equal to 0, thus making gate 1708 (which is shown in detailin FIG. 16 b) conducting. When 1708 is conducting it will provide asignal representing a ternary symbol 0 from source 1711 on output 1714.

Unit 1703 correlates the sequence provided on 1701 with sequence 1706,representing symbol 1. When this sequence is detected as being presentin the sequence provided by 1701 then the correlation unit 1703generates a signal not equal to 0, thus making gate 1709 (which is shownin detail in FIG. 16 b) conducting. When 1709 is conducting it willprovide a signal representing a ternary symbol 1 from source 1712 onoutput 1714.

Unit 1704 correlates the sequence provided by 1701 with sequence 1707,representing symbol 2. When this sequence is detected as being presentin the sequence provided by 1701 then the correlation unit 1704generates a signal not equal to 0, thus making gate 1710 (which is shownin detail in FIG. 16 b) conducting. When 1710 is conducting it willprovide a signal representing a ternary symbol 2 from source 1713 onoutput 1714.

The gates and circuits are governed by a clock signal to control theduration of the data signal. These clock signals have been omitted inthe figure to avoid making it too complex. It should be clear for thoseskilled in the art where and how the clock signals have to be applied.

The need for clock signals and use of multiple correlators can make thegeneration and detection of multi-code signals expensive. Forcorrelation it is required that to be detected sequences are in phasewith the locally generated sequence.

Another aspect of the invention is to apply the method for sequencedetection as described in U.S. Non-Provisional patent application Ser.No. 11/042,645 , filed Jan. 25, 2005, entitled MULTI-VALUED SCRAMBLINGAND DESCRAMBLING OF DIGITAL DATA ON OPTICAL DISKS AND OTHER STORAGEMEDIA and U.S. Non-Provisional patent application Ser. No. 11/065,836 ,filed Feb. 25, 2005, entitled GENERATION AND DETECTION OF NON-BINARYDIGITAL SEQUENCES, both of which are incorporated herein fully byreference.

The methods describe how a sequence generated by a Linear Feedback ShiftRegister (LFSR) based sequence generator can be detected by a relatedLFSR based descrambler. A block diagram of the detector is provided inFIG. 18. This circuit provides the same function as the one in FIG. 17.However the correlators have been replaced by detectors 1801, 1802 and1803. The individual detectors comprise a LFSR based descrambler andcircuitry that will generate a pre-determined signal when a sequencewith certain number of identical symbols has been detected.

For illustrative purposes again a ternary system will be used as anexample. It should be clear that this can be expanded to any n-valuedsolution.

FIG. 19 a shows a diagram of a LFSR based 5-element binary sequencegenerator. This sequence generator can be described by the irreduciblepolynomial of degree 5: x⁵+x²+1. The circuit has a feedback tap at thethird element of the shift register into a XOR device 1901. Thegenerated binary sequence is provided on output 1902.

FIG. 19 b shows a descrambler that will descramble the sequence providedby the generator of FIG. 19 a. The descrambler is a mirrored image ofthe generator of FIG. 19 a with a feedback tap into a XOR function 1904from the third element of the shift register. Also added is a binarydevice 1903 at the output 1906 of the descrambler executing the binaryEQUAL function on the received sequence and the sequence leaving thedescrambling unit. When the signal provided on input 1905 is generatedby the circuit of FIG. 19 a and the initial content of the shiftregisters of generator and descrambler are equal, then the signalgenerated on 1906 will be all 1s. When the initial contents are not thesame only the first 5 detected symbols may be not identical to 1.

A simple detection mechanism is to count the number of is at the output1906. If the number of 1s supersedes a predetermined number it may beassumed that the symbol represented by the specific sequence wasdetected.

In order to prevent false detections one should select the generators ofsequences representing the other 2 symbols of the ternary set in such away that they can be described by different irreducible polynomials ofdegree 5. For instance a 1 can be generated by an LFSR circuit as shownin FIG. 20 a and described by: x⁵+x³+1. Its descrambler is shown in FIG.20 b. When the descrambler of FIG. 20 b receives a sequence generated bycircuit of FIG. 19 a it will generate about 50% 0s and 50% 1s. When thedescrambler of FIG. 20 b receives a sequence generated by circuit ofFIG. 20 a it will generate a sequence of predominantly 1s, depending onthe initial content of the shift register. There is sufficientdistinction between predominantly all 1s with a sequence of about 50% 1sin for instance a sequence length of 31 elements to make a cleardetection.

For instance a 2 can be generated by an LFSR circuit as shown in FIG. 21a and described by: x⁵+x⁴+x³+x²+1. Its descrambler is shown in FIG. 21b. When the descrambler of FIG. 21 b receives a sequence generated bycircuit of FIG. 19 a or FIG. 20 a it will generate about 50% 0s and 50%1s. This is again sufficient different from all 1s to make a cleardetection.

This aspect of the invention circumvents strict requirements forin-phase generation and in-phase detection of sequences, as at most anumber of digits equivalent to the length of the shift register will notbe equal to 1 at detection. It also eliminates the requirement to createlocally generated copies of sequences for correlation purposes. It alsoallows keeping the generators running constantly in the circuit of FIG.15 without having to be concerned about initializing the content of theshift register.

It should be clear that it is possible to apply the invention to createsequences representing 2 or more symbols and detect data symbols fromsequences through descrambling.

The following patent applications, including the specifications, claimsand drawings, are hereby incorporated by reference herein, as if theywere fully set forth herein: (1) U.S. Provisional Patent Application No.60/575,948, filed on Jun. 1, 2004, entitled MULTI-VALUE CODING OFSEQUENCES AND MULTI-VALUE MEMORY DEVICES; (2) U.S. Provisional PatentApplication No. 60/668,355, filed Apr. 5, 2005, entitled IMPROVEDSEQUENCE DETECTION BY MULTI-VALUE CODING, (3) U.S. Non-Provisionalpatent application Ser. No. 10/935,960, filed on Sep. 8, 2004, entitledTERNARY AND MULTI-VALUE DIGITAL SCRAMBLERS, DESCRAMBLERS AND SEQUENCEGENERATORS; (4) U.S. Non-Provisional patent application Ser. No.10/936,181, filed Sep. 8, 2004, entitled TERNARY AND HIGHER MULTI-VALUESCRAMBLERS/DESCRAMBLERS; (5) U.S. Non-Provisional patent applicationSer. No. 10/912,954, filed Aug. 6, 2004, entitled TERNARY AND HIGHERMULTI-VALUE SCRAMBLERS/DESCRAMBLERS; (6) U.S. Non-Provisional patentapplication Ser. No. 11/042,645 , filed Jan. 25, 2005, entitledMULTI-VALUED SCRAMBLING AND DESCRAMBLING OF DIGITAL DATA ON OPTICALDISKS AND OTHER STORAGE MEDIA; (7) U.S. Non-Provisional patentapplication Ser. No. 11/000,218, filed Nov. 30, 2004, entitled SINGLEAND COMPOSITE BINARY AND MULTI-VALUED LOGIC FUNCTIONS FROM GATES ANDINVERTERS; (8) U.S. Non-Provisional patent application Ser. No.11/065,836 filed Feb. 25, 2005, entitled GENERATION AND DETECTION OFNON-BINARY DIGITAL SEQUENCES.

1. A method of coding a first sequence of binary numbers to create afirst sequence of multi-value numbers, comprising the steps ofsequentially evaluating each binary number in the sequence of binarynumbers to and: if the binary number is the first 0 encountered, placinga 0 in the first sequence of multi-value numbers; if the binary numberis the second 0 encountered, placing a 1 in the first sequence ofmulti-value numbers; if the binary number is the third 0 encountered,placing a 2 in the first sequence of multi-value numbers and beginningto look for the first 0 encountered when sequentially evaluating eachbinary number; if the binary number is the first 1 encountered, placinga 3 in the first sequence of multi-value numbers; if the binary numberis the second 1 encountered, placing a 4 in the first sequence ofmulti-value numbers; if the binary number is the third 1 encountered,placing a 5 in the first sequence of multi-value numbers and beginningto look for the first 1 encountered when sequentially evaluating eachbinary number.
 2. A method of coding a first sequence of binary numbersto create a first sequence of multi-value numbers, comprising the stepsof sequentially evaluating each binary number in the sequence of binarynumbers and creating a sequence of multi-value numbers: if the binarynumber is the first 0 encountered, placing a 0 in the first sequence ofmulti-value numbers; if the binary number is the second 0 encountered,placing a 1 in the first sequence of multi-value numbers; if the binarynumber is the third 0 encountered, placing a 2 in the first sequence ofmulti-value numbers and beginning to look for the first 0 encounteredwhen sequentially evaluating each binary number; if the binary number isthe first 1 encountered, placing a 3 in the first sequence ofmulti-value numbers; if the binary number is the second 1 encountered,placing a 4 in the first sequence of multi-value numbers; if the binarynumber is the third 1 encountered, placing a 5 in the first sequence ofmulti-value numbers and beginning to look for the first 1 encounteredwhen sequentially evaluating each binary number.
 3. A method of creatinga sequence of multi-value numbers from a first sequence of binarynumbers, comprising the steps of sequentially evaluating each binarynumber in the sequence of binary numbers and creating a sequence ofmulti-value numbers by: if the binary number is the first 0 encountered,being the first 0 in the 0rest of the binary sequence, placing a 0 inthe sequence of multi-value numbers; if the binary number is the second0 encountered, being the second 0 in the 0rest starting with the first 0of the 0rest of the binary sequence, placing a 1 in the first sequenceof multi-value numbers; if the binary number is the third 0 encountered,being the third 0 in the 0rest of the sequence starting with the first 0of the 0rest of the binary sequence, placing a 2 in the first sequenceof multi-value numbers if the binary number is the fourth 0 encountered,this 0 is now the first 0 of the new 0rest of the binary sequence,placing a 0 in the first sequence of multi-value; applying the previoussteps for the second, third and fourth 0 of the 0rest of the binarysequence to create elements in the multi-value sequence; if the binarynumber is the first 1 encountered, being the first 1 in the 1rest of thebinary sequence, placing a 3 in the sequence of multi-value numbers; ifthe binary number is the second 1 encountered, being the second 1 in the1rest starting with the first 1 of the 1rest of the binary sequence,placing a 4 in the first sequence of multi-value numbers; if the binarynumber is the third 1 encountered, being the third 1 in the 1rest of thebinary sequence starting with the first 1 of the 1 rest of the binarysequence, placing a 5 in the first sequence of multi-value numbers ifthe binary number is the fourth 1 encountered, this 1 is now the first 1of the new 1rest of the binary sequence, placing a 3 in the firstsequence of multi-value; applying the previous steps for the second,third and fourth 1 of the 1rest of the binary sequence to createelements for the multi-value sequence;
 4. A method as claimed in 3further comprising coding a locally generated binary sequence accordingto the method of claim
 3. 5. A method as claimed in 3 further comprisingcoding a received binary sequence according to the method of
 3. 6. Amethod as claimed in 3 further comprising determining the correlationbetween the multi-value coded sequences according to claims 4 and 5 insuch a manner that: a sum is initiated at 0 at the start of thecomparison process; two elements of the coded binary sequences arecompared and a number is added to the sum when the elements areidentical and a number is subtracted when the elements are different. 7.A method of creating a sequence of multi-value numbers from a firstsequence of ternary numbers, comprising the steps of sequentiallyevaluating each ternary number in the sequence of ternary numbers andcreating a sequence of multi-value numbers, as claimed in claim 3,comprising: if the ternary number is the first 0 encountered, being thefirst 0 in the 0rest of the ternary sequence, placing a 0 in thesequence of multi-value numbers; if the ternary number is the second 0encountered, being the second 0 in the 0rest starting with the first 0of the 0rest of the ternary sequence, placing a 1 in the first sequenceof multi-value numbers; if the ternary number is the third 0encountered, being the third 0 in the 0rest of the sequence startingwith the first 0 of the 0rest of the ternary sequence, placing a 2 inthe first sequence of multi-value numbers if the ternary number is thefourth 0 encountered, this 0 is now the first 0 of the new 0rest of theternary sequence, placing a 0 in the first sequence of multi-value;applying the previous steps for the second, third and fourth 0 of the0rest of the ternary sequence to create elements in the multi-valuesequence; if the ternary number is the first 1 encountered, being thefirst 1 in the 1rest of the ternary sequence, placing a 3 in thesequence of multi-value numbers; if the ternary number is the second 1encountered, being the second 1 in the 1rest starting with the first 1of the 1rest of the ternary sequence, placing a 4 in the first sequenceof multi-value numbers; if the ternary number is the third 1encountered, being the third 1 in the 1rest of the ternary sequencestarting with the first 1 of the 1rest of the ternary sequence, placinga 5 in the first sequence of multi-value numbers if the ternary numberis the fourth 1 encountered, this 1 is now the first 1 of the new 1restof the ternary sequence, placing a 3 in the first sequence ofmulti-value; applying the previous steps for the second, third andfourth 1 of the 1rest of the ternary sequence to create elements for themulti-value sequence; if the ternary number is the first 2 encountered,being the first 2 in the 2rest of the ternary sequence, placing a 6 inthe sequence of multi-value numbers; if the ternary number is the second2 encountered, being the second 2 in the 2rest starting with the first 2of the 2rest of the ternary sequence, placing a 7 in the first sequenceof multi-value numbers; if the ternary number is the third 2encountered, being the third 2 in the 2rest of the ternary sequencestarting with the first 2 of the 2rest of the ternary sequence, placinga 8 in the first sequence of multi-value numbers if the ternary numberis the fourth 2 encountered, this 2 is now the first 2 of the new 2restof the ternary sequence, placing a 6 in the first sequence ofmulti-value; applying the previous steps for the second, third andfourth 2 of the 2rest of the ternary sequence to create elements for themulti-value sequence;
 8. The method as claimed in claim 1, furthercomprising: generating a second sequence of binary numbers identical tothe first sequence of binary numbers; coding the second sequence ofbinary numbers to create a second sequence of multi-value numbers usingthe steps set forth in claim 58; determining the correlation between thefirst sequence of multi-value numbers and the second sequence ofmulti-value numbers.
 9. A method for improving the ability todistinguish between two x-valued sequences of equal length, with x aninteger greater than 2, by calculating the correlation values betweentwo sequences as claimed in claim 8, comprising: when elements incorresponding positions in each of two sequences have the same value,the contribution to the total correlation value is positive; whenelements in corresponding positions in each of two sequences havedifferent values, the contribution to the total correlation is negative.10. A method for improving the ability to distinguish between a firstand second binary sequences, the first and second binary sequenceshaving equal length, as claimed in claim 8, comprising: coding the firstbinary sequence and the second binary sequence into a first x-valuedsequence and a second x-valued sequence, respectively, using a commoncoding rule for each sequence, the common coding rule requiring that atleast 2 consecutive binary elements, either the 0 or 1, are coded into 2higher valued elements; determining the cross-correlation between thetwo coded sequences.
 11. The method as claimed in claim 10, wherein thecross-correlation is calculated by: when elements in correspondingpositions in each of two sequences have the same value, the contributionto the total correlation value is positive; when elements incorresponding positions in each of two sequences have different values,the contribution to the total correlation is negative.